#include <Transform.h>

Classes
struct	construct_from_matrix

struct	construct_from_matrix< OtherDerived, true >

Public Types
enum	{ TransformTimeDiagonalMode = ((Mode==int(Isometry))?Affine:int(Mode)) }

typedef _Scalar	Scalar
	the scalar type of the coefficients

typedef Matrix< Scalar, HDim, HDim >	MatrixType
	type of the matrix used to represent the transformation

typedef Matrix< Scalar, Dim, Dim >	LinearMatrixType
	type of the matrix used to represent the linear part of the transformation

typedef Block< MatrixType, Dim, Dim >	LinearPart
	type of read/write reference to the linear part of the transformation

typedef const Block< const MatrixType, Dim, Dim >	ConstLinearPart
	type of read/write reference to the linear part of the transformation

typedef Matrix< Scalar, Dim, 1 >	VectorType
	type of a vector

typedef Block< MatrixType, Dim, 1 >	TranslationPart
	type of a read/write reference to the translation part of the rotation

typedef const Block< const MatrixType, Dim, 1 >	ConstTranslationPart
	type of a read/write reference to the translation part of the rotation

typedef Translation< Scalar, Dim >	TranslationType
	corresponding translation type

typedef Scaling< Scalar, Dim >	ScalingType
	corresponding scaling transformation type

typedef _Scalar	Scalar
	the scalar type of the coefficients

typedef DenseIndex	Index

typedef internal::make_proper_matrix_type< Scalar, Rows, HDim, Options >::type	MatrixType
	type of the matrix used to represent the transformation

typedef const MatrixType	ConstMatrixType
	constified MatrixType

typedef Matrix< Scalar, Dim, Dim, Options >	LinearMatrixType
	type of the matrix used to represent the linear part of the transformation

typedef Block< MatrixType, Dim, Dim, int(Mode)==(AffineCompact) &&(Options &RowMajor)==0 >	LinearPart
	type of read/write reference to the linear part of the transformation

typedef const Block< ConstMatrixType, Dim, Dim, int(Mode)==(AffineCompact) &&(Options &RowMajor)==0 >	ConstLinearPart
	type of read reference to the linear part of the transformation

typedef internal::conditional< int(Mode)==int(AffineCompact), MatrixType &, Block< MatrixType, Dim, HDim > >::type	AffinePart
	type of read/write reference to the affine part of the transformation

typedef internal::conditional< int(Mode)==int(AffineCompact), const MatrixType &, const Block< const MatrixType, Dim, HDim > >::type	ConstAffinePart
	type of read reference to the affine part of the transformation

typedef Matrix< Scalar, Dim, 1 >	VectorType
	type of a vector

typedef Block< MatrixType, Dim, 1, int(Mode)==(AffineCompact)>	TranslationPart
	type of a read/write reference to the translation part of the rotation

typedef const Block< ConstMatrixType, Dim, 1, int(Mode)==(AffineCompact)>	ConstTranslationPart
	type of a read reference to the translation part of the rotation

typedef Translation< Scalar, Dim >	TranslationType
	corresponding translation type

typedef Transform< Scalar, Dim, TransformTimeDiagonalMode >	TransformTimeDiagonalReturnType
	The return type of the product between a diagonal matrix and a transform.

typedef internal::transform_take_affine_part< Transform >	take_affine_part

Public Member Functions
	EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE (_Scalar, _Dim==Dynamic ? Dynamic :(_Dim+1) *(_Dim+1)) enum

	Transform ()
	Default constructor without initialization of the coefficients. More...

	Transform (const Transform &other)

	Transform (const TranslationType &t)

	Transform (const ScalingType &s)

template<typename Derived >
	Transform (const RotationBase< Derived, Dim > &r)

Transform &	operator= (const Transform &other)

template<typename OtherDerived >
	Transform (const MatrixBase< OtherDerived > &other)
	Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. More...

template<typename OtherDerived >
Transform &	operator= (const MatrixBase< OtherDerived > &other)
	Set `*this` from a (Dim+1)^2 matrix. More...

Scalar	operator() (int row, int col) const
	shortcut for m_matrix(row,col); More...

Scalar &	operator() (int row, int col)
	shortcut for m_matrix(row,col); More...

const MatrixType &	matrix () const

MatrixType &	matrix ()

ConstLinearPart	linear () const

LinearPart	linear ()

ConstTranslationPart	translation () const

TranslationPart	translation ()

template<typename OtherDerived >
const ei_transform_product_impl< OtherDerived, _Dim, _Dim+1 >::ResultType	operator* (const MatrixBase< OtherDerived > &other) const

const Transform	operator* (const Transform &other) const
	Contatenates two transformations.

void	setIdentity ()

template<typename OtherDerived >
Transform &	scale (const MatrixBase< OtherDerived > &other)

template<typename OtherDerived >
Transform &	prescale (const MatrixBase< OtherDerived > &other)

Transform &	scale (Scalar s)
	Applies on the right a uniform scale of a factor c to `this` and returns a reference to `this`. More...

Transform &	prescale (Scalar s)
	Applies on the left a uniform scale of a factor c to `this` and returns a reference to `this`. More...

template<typename OtherDerived >
Transform &	translate (const MatrixBase< OtherDerived > &other)

template<typename OtherDerived >
Transform &	pretranslate (const MatrixBase< OtherDerived > &other)

template<typename RotationType >
Transform &	rotate (const RotationType &rotation)

template<typename RotationType >
Transform &	prerotate (const RotationType &rotation)

Transform &	shear (Scalar sx, Scalar sy)
	Applies on the right the shear transformation represented by the vector other to `this` and returns a reference to `this`. More...

Transform &	preshear (Scalar sx, Scalar sy)
	Applies on the left the shear transformation represented by the vector other to `this` and returns a reference to `this`. More...

Transform &	operator= (const TranslationType &t)

Transform &	*operator=** (const TranslationType &t)

Transform	operator* (const TranslationType &t) const

Transform &	operator= (const ScalingType &t)

Transform &	*operator=** (const ScalingType &s)

Transform	operator* (const ScalingType &s) const

template<typename Derived >
Transform &	operator= (const RotationBase< Derived, Dim > &r)

template<typename Derived >
Transform &	*operator=** (const RotationBase< Derived, Dim > &r)

template<typename Derived >
Transform	operator* (const RotationBase< Derived, Dim > &r) const

LinearMatrixType	rotation () const

template<typename RotationMatrixType , typename ScalingMatrixType >
void	computeRotationScaling (RotationMatrixType rotation, ScalingMatrixType scaling) const
	decomposes the linear part of the transformation as a product rotation x scaling, the scaling being not necessarily positive. More...

template<typename ScalingMatrixType , typename RotationMatrixType >
void	computeScalingRotation (ScalingMatrixType scaling, RotationMatrixType rotation) const
	decomposes the linear part of the transformation as a product rotation x scaling, the scaling being not necessarily positive. More...

template<typename PositionDerived , typename OrientationType , typename ScaleDerived >
Transform &	fromPositionOrientationScale (const MatrixBase< PositionDerived > &position, const OrientationType &orientation, const MatrixBase< ScaleDerived > &scale)

const MatrixType	inverse (TransformTraits traits=Affine) const

const Scalar *	data () const

Scalar *	data ()

template<typename NewScalarType >
internal::cast_return_type< Transform, Transform< NewScalarType, Dim > >::type	cast () const

template<typename OtherScalarType >
	Transform (const Transform< OtherScalarType, Dim > &other)
	Copy constructor with scalar type conversion.

bool	isApprox (const Transform &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const

	EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE (_Scalar, _Dim==Dynamic ? Dynamic :(_Dim+1) *(_Dim+1)) enum

	Transform ()
	Default constructor without initialization of the meaningful coefficients. More...

	Transform (const Transform &other)

	Transform (const TranslationType &t)

	Transform (const UniformScaling< Scalar > &s)

template<typename Derived >
	Transform (const RotationBase< Derived, Dim > &r)

Transform &	operator= (const Transform &other)

template<typename OtherDerived >
	Transform (const EigenBase< OtherDerived > &other)
	Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. More...

template<typename OtherDerived >
Transform &	operator= (const EigenBase< OtherDerived > &other)
	Set `*this` from a Dim^2 or (Dim+1)^2 matrix. More...

template<int OtherOptions>
	Transform (const Transform< Scalar, Dim, Mode, OtherOptions > &other)

template<int OtherMode, int OtherOptions>
	Transform (const Transform< Scalar, Dim, OtherMode, OtherOptions > &other)

template<typename OtherDerived >
	Transform (const ReturnByValue< OtherDerived > &other)

template<typename OtherDerived >
Transform &	operator= (const ReturnByValue< OtherDerived > &other)

Scalar	operator() (Index row, Index col) const
	shortcut for m_matrix(row,col); More...

Scalar &	operator() (Index row, Index col)
	shortcut for m_matrix(row,col); More...

const MatrixType &	matrix () const

MatrixType &	matrix ()

ConstLinearPart	linear () const

LinearPart	linear ()

ConstAffinePart	affine () const

AffinePart	affine ()

ConstTranslationPart	translation () const

TranslationPart	translation ()

template<typename OtherDerived >
EIGEN_STRONG_INLINE const OtherDerived::PlainObject	operator* (const EigenBase< OtherDerived > &other) const

template<typename DiagonalDerived >
const TransformTimeDiagonalReturnType	operator* (const DiagonalBase< DiagonalDerived > &b) const

template<typename OtherDerived >
Transform &	*operator=** (const EigenBase< OtherDerived > &other)

const Transform	operator* (const Transform &other) const
	Concatenates two transformations.

template<int OtherMode, int OtherOptions>
internal::transform_transform_product_impl< Transform, Transform< Scalar, Dim, OtherMode, OtherOptions > >::ResultType	operator* (const Transform< Scalar, Dim, OtherMode, OtherOptions > &other) const
	Concatenates two different transformations.

void	setIdentity ()

template<typename OtherDerived >
Transform &	scale (const MatrixBase< OtherDerived > &other)

template<typename OtherDerived >
Transform &	prescale (const MatrixBase< OtherDerived > &other)

Transform &	scale (const Scalar &s)
	Applies on the right a uniform scale of a factor c to `this` and returns a reference to `this`. More...

Transform &	prescale (const Scalar &s)
	Applies on the left a uniform scale of a factor c to `this` and returns a reference to `this`. More...

template<typename OtherDerived >
Transform &	translate (const MatrixBase< OtherDerived > &other)

template<typename OtherDerived >
Transform &	pretranslate (const MatrixBase< OtherDerived > &other)

template<typename RotationType >
Transform &	rotate (const RotationType &rotation)

template<typename RotationType >
Transform &	prerotate (const RotationType &rotation)

Transform &	shear (const Scalar &sx, const Scalar &sy)
	Applies on the right the shear transformation represented by the vector other to `this` and returns a reference to `this`. More...

Transform &	preshear (const Scalar &sx, const Scalar &sy)
	Applies on the left the shear transformation represented by the vector other to `this` and returns a reference to `this`. More...

Transform &	operator= (const TranslationType &t)

Transform &	*operator=** (const TranslationType &t)

Transform	operator* (const TranslationType &t) const

Transform &	operator= (const UniformScaling< Scalar > &t)

Transform &	*operator=** (const UniformScaling< Scalar > &s)

Transform< Scalar, Dim,(int(Mode)==int(Isometry)?int(Affine):int(Mode))>	operator* (const UniformScaling< Scalar > &s) const

Transform &	*operator=** (const DiagonalMatrix< Scalar, Dim > &s)

template<typename Derived >
Transform &	operator= (const RotationBase< Derived, Dim > &r)

template<typename Derived >
Transform &	*operator=** (const RotationBase< Derived, Dim > &r)

template<typename Derived >
Transform	operator* (const RotationBase< Derived, Dim > &r) const

const LinearMatrixType	rotation () const

template<typename RotationMatrixType , typename ScalingMatrixType >
void	computeRotationScaling (RotationMatrixType rotation, ScalingMatrixType scaling) const

template<typename ScalingMatrixType , typename RotationMatrixType >
void	computeScalingRotation (ScalingMatrixType scaling, RotationMatrixType rotation) const

template<typename PositionDerived , typename OrientationType , typename ScaleDerived >
Transform &	fromPositionOrientationScale (const MatrixBase< PositionDerived > &position, const OrientationType &orientation, const MatrixBase< ScaleDerived > &scale)

Transform	inverse (TransformTraits traits=(TransformTraits) Mode) const

const Scalar *	data () const

Scalar *	data ()

template<typename NewScalarType >
internal::cast_return_type< Transform, Transform< NewScalarType, Dim, Mode, Options > >::type	cast () const

template<typename OtherScalarType >
	Transform (const Transform< OtherScalarType, Dim, Mode, Options > &other)
	Copy constructor with scalar type conversion.

bool	isApprox (const Transform &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const

void	makeAffine ()
	Sets the last row to [0 ... More...

Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim, Dim >	linearExt ()

const Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim, Dim >	linearExt () const

Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim, 1 >	translationExt ()

const Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim, 1 >	translationExt () const

template<typename OtherDerived >
Transform< Scalar, Dim > &	scale (const MatrixBase< OtherDerived > &other)
	Applies on the right the non uniform scale transformation represented by the vector other to `this` and returns a reference to `this`. More...

template<typename OtherDerived >
Transform< Scalar, Dim > &	prescale (const MatrixBase< OtherDerived > &other)
	Applies on the left the non uniform scale transformation represented by the vector other to `this` and returns a reference to `this`. More...

template<typename OtherDerived >
Transform< Scalar, Dim > &	translate (const MatrixBase< OtherDerived > &other)
	Applies on the right the translation matrix represented by the vector other to `this` and returns a reference to `this`. More...

template<typename OtherDerived >
Transform< Scalar, Dim > &	pretranslate (const MatrixBase< OtherDerived > &other)
	Applies on the left the translation matrix represented by the vector other to `this` and returns a reference to `this`. More...

template<typename RotationType >
Transform< Scalar, Dim > &	rotate (const RotationType &rotation)
	Applies on the right the rotation represented by the rotation rotation to `this` and returns a reference to `this`. More...

template<typename RotationType >
Transform< Scalar, Dim > &	prerotate (const RotationType &rotation)
	Applies on the left the rotation represented by the rotation rotation to `this` and returns a reference to `this`. More...

template<typename Derived >
Transform< Scalar, Dim > &	operator= (const RotationBase< Derived, Dim > &r)

template<typename Derived>
Transform< Scalar, Dim >	operator* (const RotationBase< Derived, Dim > &r) const

template<typename PositionDerived , typename OrientationType , typename ScaleDerived >
Transform< Scalar, Dim > &	fromPositionOrientationScale (const MatrixBase< PositionDerived > &position, const OrientationType &orientation, const MatrixBase< ScaleDerived > &scale)
	Convenient method to set `*this` from a position, orientation and scale of a 3D object.

template<typename OtherDerived >
Transform< Scalar, Dim, Mode, Options > &	scale (const MatrixBase< OtherDerived > &other)
	Applies on the right the non uniform scale transformation represented by the vector other to `this` and returns a reference to `this`. More...

template<typename OtherDerived >
Transform< Scalar, Dim, Mode, Options > &	prescale (const MatrixBase< OtherDerived > &other)
	Applies on the left the non uniform scale transformation represented by the vector other to `this` and returns a reference to `this`. More...

template<typename OtherDerived >
Transform< Scalar, Dim, Mode, Options > &	translate (const MatrixBase< OtherDerived > &other)
	Applies on the right the translation matrix represented by the vector other to `this` and returns a reference to `this`. More...

template<typename OtherDerived >
Transform< Scalar, Dim, Mode, Options > &	pretranslate (const MatrixBase< OtherDerived > &other)
	Applies on the left the translation matrix represented by the vector other to `this` and returns a reference to `this`. More...

template<typename RotationType >
Transform< Scalar, Dim, Mode, Options > &	rotate (const RotationType &rotation)
	Applies on the right the rotation represented by the rotation rotation to `this` and returns a reference to `this`. More...

template<typename RotationType >
Transform< Scalar, Dim, Mode, Options > &	prerotate (const RotationType &rotation)
	Applies on the left the rotation represented by the rotation rotation to `this` and returns a reference to `this`. More...

template<typename Derived >
Transform< Scalar, Dim, Mode, Options > &	operator= (const RotationBase< Derived, Dim > &r)

template<typename Derived>
Transform< Scalar, Dim, Mode, Options >	operator* (const RotationBase< Derived, Dim > &r) const

template<typename PositionDerived , typename OrientationType , typename ScaleDerived >
Transform< Scalar, Dim, Mode, Options > &	fromPositionOrientationScale (const MatrixBase< PositionDerived > &position, const OrientationType &orientation, const MatrixBase< ScaleDerived > &scale)
	Convenient method to set `*this` from a position, orientation and scale of a 3D object.

Static Public Member Functions
static const MatrixType::IdentityReturnType	Identity ()

static const Transform	Identity ()
	Returns an identity transformation. More...

Static Protected Member Functions
static EIGEN_STRONG_INLINE void	check_template_params ()

Protected Attributes
MatrixType	m_matrix

Friends
template<typename OtherDerived >
const ProductReturnType< OtherDerived, MatrixType >::Type	operator* (const MatrixBase< OtherDerived > &a, const Transform &b)

Transform	operator* (const LinearMatrixType &mat, const Transform &t)

template<typename OtherDerived >
const internal::transform_left_product_impl< OtherDerived, Mode, Options, _Dim, _Dim+1 >::ResultType	operator* (const EigenBase< OtherDerived > &a, const Transform &b)

template<typename DiagonalDerived >
TransformTimeDiagonalReturnType	operator* (const DiagonalBase< DiagonalDerived > &a, const Transform &b)

Detailed Description

template<typename _Scalar, int _Dim>
class Eigen::Transform< _Scalar, _Dim >

Represents an homogeneous transformation in a N dimensional space

Parameters

_Scalar	the scalar type, i.e., the type of the coefficients
_Dim	the dimension of the space

The homography is internally represented and stored as a (Dim+1)^2 matrix which is available through the matrix() method.

Conversion methods from/to Qt's QMatrix and QTransform are available if the preprocessor token EIGEN_QT_SUPPORT is defined.

See also: class Matrix, class Quaternion

Represents an homogeneous transformation in a N dimensional space

Template Parameters

_Scalar	the scalar type, i.e., the type of the coefficients
_Dim	the dimension of the space
_Mode	the type of the transformation. Can be: Affine: the transformation is stored as a (Dim+1)^2 matrix, where the last row is assumed to be [0 ... 0 1]. AffineCompact: the transformation is stored as a (Dim)x(Dim+1) matrix. Projective: the transformation is stored as a (Dim+1)^2 matrix without any assumption.
_Options	has the same meaning as in class Matrix. It allows to specify DontAlign and/or RowMajor. These Options are passed directly to the underlying matrix type.

The homography is internally represented and stored by a matrix which is available through the matrix() method. To understand the behavior of this class you have to think a Transform object as its internal matrix representation. The chosen convention is right multiply:

v' = T * v

Therefore, an affine transformation matrix M is shaped like this:

\( \left( \begin{array}{cc} linear & translation\\ 0 ... 0 & 1 \end{array} \right) \)

Note that for a projective transformation the last row can be anything, and then the interpretation of different parts might be sightly different.

However, unlike a plain matrix, the Transform class provides many features simplifying both its assembly and usage. In particular, it can be composed with any other transformations (Transform,Translation,RotationBase,DiagonalMatrix) and can be directly used to transform implicit homogeneous vectors. All these operations are handled via the operator*. For the composition of transformations, its principle consists to first convert the right/left hand sides of the product to a compatible (Dim+1)^2 matrix and then perform a pure matrix product. Of course, internally, operator* tries to perform the minimal number of operations according to the nature of each terms. Likewise, when applying the transform to points, the latters are automatically promoted to homogeneous vectors before doing the matrix product. The conventions to homogeneous representations are performed as follow:

Translation t (Dim)x(1): \( \left( \begin{array}{cc} I & t \\ 0\,...\,0 & 1 \end{array} \right) \)

Rotation R (Dim)x(Dim): \( \left( \begin{array}{cc} R & 0\\ 0\,...\,0 & 1 \end{array} \right) \)

Scaling DiagonalMatrix S (Dim)x(Dim): \( \left( \begin{array}{cc} S & 0\\ 0\,...\,0 & 1 \end{array} \right) \)

Column point v (Dim)x(1): \( \left( \begin{array}{c} v\\ 1 \end{array} \right) \)

Set of column points V1...Vn (Dim)x(n): \( \left( \begin{array}{ccc} v_1 & ... & v_n\\ 1 & ... & 1 \end{array} \right) \)

The concatenation of a Transform object with any kind of other transformation always returns a Transform object.

A little exception to the "as pure matrix product" rule is the case of the transformation of non homogeneous vectors by an affine transformation. In that case the last matrix row can be ignored, and the product returns non homogeneous vectors.

Since, for instance, a Dim x Dim matrix is interpreted as a linear transformation, it is not possible to directly transform Dim vectors stored in a Dim x Dim matrix. The solution is either to use a Dim x Dynamic matrix or explicitly request a vector transformation by making the vector homogeneous:

m' = T * m.colwise().homogeneous();

Note that there is zero overhead.

Conversion methods from/to Qt's QMatrix and QTransform are available if the preprocessor token EIGEN_QT_SUPPORT is defined.

This class can be extended with the help of the plugin mechanism described on the page Customizing/Extending Eigen by defining the preprocessor symbol EIGEN_TRANSFORM_PLUGIN.

See also: class Matrix, class Quaternion

Constructor & Destructor Documentation

§ Transform() [1/4]

template<typename _Scalar, int _Dim>

Eigen::Transform< _Scalar, _Dim >::Transform ( )

inline

Default constructor without initialization of the coefficients.

§ Transform() [2/4]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Eigen::Transform< _Scalar, _Dim >::Transform ( const MatrixBase< OtherDerived > & other )

inlineexplicit

Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix.

§ Transform() [3/4]

template<typename _Scalar, int _Dim>

Eigen::Transform< _Scalar, _Dim >::Transform ( )

inline

Default constructor without initialization of the meaningful coefficients.

If Mode==Affine, then the last row is set to [0 ... 0 1]

§ Transform() [4/4]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Eigen::Transform< _Scalar, _Dim >::Transform ( const EigenBase< OtherDerived > & other )

inlineexplicit

Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix.

Member Function Documentation

§ affine() [1/2]

template<typename _Scalar, int _Dim>

ConstAffinePart Eigen::Transform< _Scalar, _Dim >::affine ( ) const

inline

Returns: a read-only expression of the Dim x HDim affine part of the transformation

§ affine() [2/2]

template<typename _Scalar, int _Dim>

AffinePart Eigen::Transform< _Scalar, _Dim >::affine ( )

inline

Returns: a writable expression of the Dim x HDim affine part of the transformation

§ cast() [1/2]

template<typename _Scalar, int _Dim>

template<typename NewScalarType >

internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type Eigen::Transform< _Scalar, _Dim >::cast ( ) const

inline

Returns: *this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

§ cast() [2/2]

template<typename _Scalar, int _Dim>

template<typename NewScalarType >

internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type Eigen::Transform< _Scalar, _Dim >::cast ( ) const

inline

Returns: *this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

§ computeRotationScaling()

template<typename Scalar , int Dim, int Mode, int Options>

template<typename RotationMatrixType , typename ScalingMatrixType >

void Eigen::Transform< Scalar, Dim, Mode, Options >::computeRotationScaling	(	RotationMatrixType *	rotation,
		ScalingMatrixType *	scaling
	)		const

decomposes the linear part of the transformation as a product rotation x scaling, the scaling being not necessarily positive.

If either pointer is zero, the corresponding computation is skipped.

See also: computeScalingRotation(), rotation(), class SVD

If either pointer is zero, the corresponding computation is skipped.

See also: computeScalingRotation(), rotation(), class SVD

§ computeScalingRotation()

template<typename Scalar , int Dim, int Mode, int Options>

template<typename ScalingMatrixType , typename RotationMatrixType >

void Eigen::Transform< Scalar, Dim, Mode, Options >::computeScalingRotation	(	ScalingMatrixType *	scaling,
		RotationMatrixType *	rotation
	)		const

decomposes the linear part of the transformation as a product rotation x scaling, the scaling being not necessarily positive.

If either pointer is zero, the corresponding computation is skipped.

See also: computeRotationScaling(), rotation(), class SVD

If either pointer is zero, the corresponding computation is skipped.

See also: computeRotationScaling(), rotation(), class SVD

§ data() [1/4]

template<typename _Scalar, int _Dim>

const Scalar* Eigen::Transform< _Scalar, _Dim >::data ( ) const

inline

Returns: a const pointer to the column major internal matrix

§ data() [2/4]

template<typename _Scalar, int _Dim>

Scalar* Eigen::Transform< _Scalar, _Dim >::data ( )

inline

Returns: a non-const pointer to the column major internal matrix

§ data() [3/4]

template<typename _Scalar, int _Dim>

const Scalar* Eigen::Transform< _Scalar, _Dim >::data ( ) const

inline

Returns: a const pointer to the column major internal matrix

§ data() [4/4]

template<typename _Scalar, int _Dim>

Scalar* Eigen::Transform< _Scalar, _Dim >::data ( )

inline

Returns: a non-const pointer to the column major internal matrix

§ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE() [1/2]

template<typename _Scalar, int _Dim>

Eigen::Transform< _Scalar, _Dim >::EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE	(	_Scalar	,
		_Dim	= `=Dynamic ? Dynamic : (_Dim+1)*(_Dim+1)`
	)

inline

< space dimension in which the transformation holds

< size of a respective homogeneous vector

§ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE() [2/2]

template<typename _Scalar, int _Dim>

Eigen::Transform< _Scalar, _Dim >::EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE	(	_Scalar	,
		_Dim	= `=Dynamic ? Dynamic : (_Dim+1)*(_Dim+1)`
	)

inline

< space dimension in which the transformation holds

< size of a respective homogeneous vector

§ Identity()

template<typename _Scalar, int _Dim>

static const Transform Eigen::Transform< _Scalar, _Dim >::Identity ( )

inlinestatic

Returns an identity transformation.

Todo:: In the future this function should be returning a Transform expression.

§ inverse()

template<typename Scalar , int Dim, int Mode, int Options>

Transform< Scalar, Dim, Mode, Options > Eigen::Transform< Scalar, Dim, Mode, Options >::inverse ( TransformTraits hint = Affine ) const

inline

Returns: the inverse transformation matrix according to some given knowledge on *this.

Parameters

traits

allows to optimize the inversion process when the transformion is known to be not a general transformation. The possible values are:

Projective if the transformation is not necessarily affine, i.e., if the last row is not guaranteed to be [0 ... 0 1]
Affine is the default, the last row is assumed to be [0 ... 0 1]
Isometry if the transformation is only a concatenations of translations and rotations.

Warning: unless traits is always set to NoShear or NoScaling, this function requires the generic inverse method of MatrixBase defined in the LU module. If you forget to include this module, then you will get hard to debug linking errors.

See also: MatrixBase::inverse()

Returns: the inverse transformation according to some given knowledge on *this.

Parameters

hint

allows to optimize the inversion process when the transformation is known to be not a general transformation (optional). The possible values are:

Projective if the transformation is not necessarily affine, i.e., if the last row is not guaranteed to be [0 ... 0 1]
Affine if the last row can be assumed to be [0 ... 0 1]
Isometry if the transformation is only a concatenations of translations and rotations. The default is the template class parameter Mode.

Warning: unless traits is always set to NoShear or NoScaling, this function requires the generic inverse method of MatrixBase defined in the LU module. If you forget to include this module, then you will get hard to debug linking errors.

See also: MatrixBase::inverse()

§ isApprox() [1/2]

template<typename _Scalar, int _Dim>

bool Eigen::Transform< _Scalar, _Dim >::isApprox	(	const Transform< _Scalar, _Dim > &	other,
		typename NumTraits< Scalar >::Real	prec = `precision<Scalar>()`
	)		const

inline

Returns: true if *this is approximately equal to other, within the precision determined by prec.

See also: MatrixBase::isApprox()

§ isApprox() [2/2]

template<typename _Scalar, int _Dim>

bool Eigen::Transform< _Scalar, _Dim >::isApprox	(	const Transform< _Scalar, _Dim > &	other,
		const typename NumTraits< Scalar >::Real &	prec = `NumTraits<Scalar>::dummy_precision()`
	)		const

inline

Returns: true if *this is approximately equal to other, within the precision determined by prec.

See also: MatrixBase::isApprox()

§ linear() [1/4]

template<typename _Scalar, int _Dim>

ConstLinearPart Eigen::Transform< _Scalar, _Dim >::linear ( ) const

inline

Returns: a read-only expression of the linear (linear) part of the transformation

§ linear() [2/4]

template<typename _Scalar, int _Dim>

LinearPart Eigen::Transform< _Scalar, _Dim >::linear ( )

inline

Returns: a writable expression of the linear (linear) part of the transformation

§ linear() [3/4]

template<typename _Scalar, int _Dim>

ConstLinearPart Eigen::Transform< _Scalar, _Dim >::linear ( ) const

inline

Returns: a read-only expression of the linear part of the transformation

§ linear() [4/4]

template<typename _Scalar, int _Dim>

LinearPart Eigen::Transform< _Scalar, _Dim >::linear ( )

inline

Returns: a writable expression of the linear part of the transformation

§ makeAffine()

template<typename _Scalar, int _Dim>

void Eigen::Transform< _Scalar, _Dim >::makeAffine ( )

inline

Sets the last row to [0 ...

0 1]

§ matrix() [1/4]

template<typename _Scalar, int _Dim>

const MatrixType& Eigen::Transform< _Scalar, _Dim >::matrix ( ) const

inline

Returns: a read-only expression of the transformation matrix

§ matrix() [2/4]

template<typename _Scalar, int _Dim>

MatrixType& Eigen::Transform< _Scalar, _Dim >::matrix ( )

inline

Returns: a writable expression of the transformation matrix

§ matrix() [3/4]

template<typename _Scalar, int _Dim>

const MatrixType& Eigen::Transform< _Scalar, _Dim >::matrix ( ) const

inline

Returns: a read-only expression of the transformation matrix

§ matrix() [4/4]

template<typename _Scalar, int _Dim>

MatrixType& Eigen::Transform< _Scalar, _Dim >::matrix ( )

inline

Returns: a writable expression of the transformation matrix

§ operator()() [1/4]

template<typename _Scalar, int _Dim>

Scalar Eigen::Transform< _Scalar, _Dim >::operator()	(	int	row,
		int	col
	)		const

inline

shortcut for m_matrix(row,col);

See also: MatrixBase::operaror(int,int) const

§ operator()() [2/4]

template<typename _Scalar, int _Dim>

Scalar& Eigen::Transform< _Scalar, _Dim >::operator()	(	int	row,
		int	col
	)

inline

shortcut for m_matrix(row,col);

See also: MatrixBase::operaror(int,int)

§ operator()() [3/4]

template<typename _Scalar, int _Dim>

Scalar Eigen::Transform< _Scalar, _Dim >::operator()	(	Index	row,
		Index	col
	)		const

inline

shortcut for m_matrix(row,col);

See also: MatrixBase::operator(Index,Index) const

§ operator()() [4/4]

template<typename _Scalar, int _Dim>

Scalar& Eigen::Transform< _Scalar, _Dim >::operator()	(	Index	row,
		Index	col
	)

inline

shortcut for m_matrix(row,col);

See also: MatrixBase::operator(Index,Index)

§ operator*() [1/3]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

const ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType Eigen::Transform< _Scalar, _Dim >::operator* ( const MatrixBase< OtherDerived > & other ) const

inline

Returns: an expression of the product between the transform *this and a matrix expression other

The right hand side other might be either:

a vector of size Dim,
an homogeneous vector of size Dim+1,
a transformation matrix of size Dim+1 x Dim+1.

§ operator*() [2/3]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

EIGEN_STRONG_INLINE const OtherDerived::PlainObject Eigen::Transform< _Scalar, _Dim >::operator* ( const EigenBase< OtherDerived > & other ) const

inline

Returns: an expression of the product between the transform *this and a matrix expression other.

The right-hand-side other can be either:

an homogeneous vector of size Dim+1,
a set of homogeneous vectors of size Dim+1 x N,
a transformation matrix of size Dim+1 x Dim+1.

Moreover, if *this represents an affine transformation (i.e., Mode!=Projective), then other can also be:

a point of size Dim (computes:
this->linear() * other + this->translation()
),
a set of N points as a Dim x N matrix (computes:
(this->linear() * other).colwise() + this->translation()
),

In all cases, the return type is a matrix or vector of same sizes as the right-hand-side other.

If you want to interpret other as a linear or affine transformation, then first convert it to a Transform<> type, or do your own cooking.

Finally, if you want to apply Affine transformations to vectors, then explicitly apply the linear part only:

Affine3f A;
Vector3f v1, v2;
v2 = A.linear() * v1;

§ operator*() [3/3]

template<typename _Scalar, int _Dim>

template<typename DiagonalDerived >

const TransformTimeDiagonalReturnType Eigen::Transform< _Scalar, _Dim >::operator* ( const DiagonalBase< DiagonalDerived > & b ) const

inline

Returns: The product expression of a transform a times a diagonal matrix b

The rhs diagonal matrix is interpreted as an affine scaling transformation. The product results in a Transform of the same type (mode) as the lhs only if the lhs mode is no isometry. In that case, the returned transform is an affinity.

§ operator=() [1/2]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Transform& Eigen::Transform< _Scalar, _Dim >::operator= ( const MatrixBase< OtherDerived > & other )

inline

Set *this from a (Dim+1)^2 matrix.

§ operator=() [2/2]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Transform& Eigen::Transform< _Scalar, _Dim >::operator= ( const EigenBase< OtherDerived > & other )

inline

Set *this from a Dim^2 or (Dim+1)^2 matrix.

§ prerotate() [1/2]

template<typename _Scalar, int _Dim>

template<typename RotationType >

Transform<Scalar,Dim>& Eigen::Transform< _Scalar, _Dim >::prerotate ( const RotationType & rotation )

Applies on the left the rotation represented by the rotation rotation to *this and returns a reference to *this.

See rotate() for further details.

See also: rotate()

§ prerotate() [2/2]

template<typename _Scalar, int _Dim>

template<typename RotationType >

Transform<Scalar,Dim,Mode,Options>& Eigen::Transform< _Scalar, _Dim >::prerotate ( const RotationType & rotation )

Applies on the left the rotation represented by the rotation rotation to *this and returns a reference to *this.

See rotate() for further details.

See also: rotate()

§ prescale() [1/4]

template<typename Scalar , int Dim>

Transform< Scalar, Dim > & Eigen::Transform< Scalar, Dim >::prescale ( Scalar s )

inline

Applies on the left a uniform scale of a factor c to *this and returns a reference to *this.

See also: scale(Scalar)

§ prescale() [2/4]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Transform<Scalar,Dim>& Eigen::Transform< _Scalar, _Dim >::prescale ( const MatrixBase< OtherDerived > & other )

Applies on the left the non uniform scale transformation represented by the vector other to *this and returns a reference to *this.

See also: scale()

§ prescale() [3/4]

template<typename Scalar , int Dim, int Mode, int Options>

Transform< Scalar, Dim, Mode, Options > & Eigen::Transform< Scalar, Dim, Mode, Options >::prescale ( const Scalar & s )

inline

Applies on the left a uniform scale of a factor c to *this and returns a reference to *this.

See also: scale(Scalar)

§ prescale() [4/4]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Transform<Scalar,Dim,Mode,Options>& Eigen::Transform< _Scalar, _Dim >::prescale ( const MatrixBase< OtherDerived > & other )

Applies on the left the non uniform scale transformation represented by the vector other to *this and returns a reference to *this.

See also: scale()

§ preshear() [1/2]

template<typename Scalar , int Dim>

Transform< Scalar, Dim > & Eigen::Transform< Scalar, Dim >::preshear	(	Scalar	sx,
		Scalar	sy
	)

Applies on the left the shear transformation represented by the vector other to *this and returns a reference to *this.

Warning: 2D only.

See also: shear()

§ preshear() [2/2]

template<typename Scalar , int Dim, int Mode, int Options>

Transform< Scalar, Dim, Mode, Options > & Eigen::Transform< Scalar, Dim, Mode, Options >::preshear	(	const Scalar &	sx,
		const Scalar &	sy
	)

Applies on the left the shear transformation represented by the vector other to *this and returns a reference to *this.

Warning: 2D only.

See also: shear()

§ pretranslate() [1/2]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Transform<Scalar,Dim>& Eigen::Transform< _Scalar, _Dim >::pretranslate ( const MatrixBase< OtherDerived > & other )

Applies on the left the translation matrix represented by the vector other to *this and returns a reference to *this.

See also: translate()

§ pretranslate() [2/2]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Transform<Scalar,Dim,Mode,Options>& Eigen::Transform< _Scalar, _Dim >::pretranslate ( const MatrixBase< OtherDerived > & other )

Applies on the left the translation matrix represented by the vector other to *this and returns a reference to *this.

See also: translate()

§ rotate() [1/2]

template<typename _Scalar, int _Dim>

template<typename RotationType >

Transform<Scalar,Dim>& Eigen::Transform< _Scalar, _Dim >::rotate ( const RotationType & rotation )

Applies on the right the rotation represented by the rotation rotation to *this and returns a reference to *this.

The template parameter RotationType is the type of the rotation which must be known by ei_toRotationMatrix<>.

Natively supported types includes:

any scalar (2D),
a Dim x Dim matrix expression,
a Quaternion (3D),
a AngleAxis (3D)

This mechanism is easily extendable to support user types such as Euler angles, or a pair of Quaternion for 4D rotations.

See also: rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType)

§ rotate() [2/2]

template<typename _Scalar, int _Dim>

template<typename RotationType >

Transform<Scalar,Dim,Mode,Options>& Eigen::Transform< _Scalar, _Dim >::rotate ( const RotationType & rotation )

Applies on the right the rotation represented by the rotation rotation to *this and returns a reference to *this.

The template parameter RotationType is the type of the rotation which must be known by internal::toRotationMatrix<>.

Natively supported types includes:

any scalar (2D),
a Dim x Dim matrix expression,
a Quaternion (3D),
a AngleAxis (3D)

This mechanism is easily extendable to support user types such as Euler angles, or a pair of Quaternion for 4D rotations.

See also: rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType)

§ rotation()

template<typename Scalar , int Dim, int Mode, int Options>

const Transform< Scalar, Dim, Mode, Options >::LinearMatrixType Eigen::Transform< Scalar, Dim, Mode, Options >::rotation ( ) const

Returns: the rotation part of the transformation

See also: computeRotationScaling(), computeScalingRotation(), class SVD

Returns: the rotation part of the transformation

See also: computeRotationScaling(), computeScalingRotation(), class SVD

§ scale() [1/4]

template<typename Scalar , int Dim>

Transform< Scalar, Dim > & Eigen::Transform< Scalar, Dim >::scale ( Scalar s )

inline

Applies on the right a uniform scale of a factor c to *this and returns a reference to *this.

See also: prescale(Scalar)

§ scale() [2/4]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Transform<Scalar,Dim>& Eigen::Transform< _Scalar, _Dim >::scale ( const MatrixBase< OtherDerived > & other )

Applies on the right the non uniform scale transformation represented by the vector other to *this and returns a reference to *this.

See also: prescale()

§ scale() [3/4]

template<typename Scalar , int Dim, int Mode, int Options>

Transform< Scalar, Dim, Mode, Options > & Eigen::Transform< Scalar, Dim, Mode, Options >::scale ( const Scalar & s )

inline

Applies on the right a uniform scale of a factor c to *this and returns a reference to *this.

See also: prescale(Scalar)

§ scale() [4/4]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Transform<Scalar,Dim,Mode,Options>& Eigen::Transform< _Scalar, _Dim >::scale ( const MatrixBase< OtherDerived > & other )

Applies on the right the non uniform scale transformation represented by the vector other to *this and returns a reference to *this.

See also: prescale()

§ setIdentity() [1/2]

template<typename _Scalar, int _Dim>

void Eigen::Transform< _Scalar, _Dim >::setIdentity ( )

inline

See also: MatrixBase::setIdentity()

§ setIdentity() [2/2]

template<typename _Scalar, int _Dim>

void Eigen::Transform< _Scalar, _Dim >::setIdentity ( )

inline

See also: MatrixBase::setIdentity()

§ shear() [1/2]

template<typename Scalar , int Dim>

Transform< Scalar, Dim > & Eigen::Transform< Scalar, Dim >::shear	(	Scalar	sx,
		Scalar	sy
	)

Applies on the right the shear transformation represented by the vector other to *this and returns a reference to *this.

Warning: 2D only.

See also: preshear()

§ shear() [2/2]

template<typename Scalar , int Dim, int Mode, int Options>

Transform< Scalar, Dim, Mode, Options > & Eigen::Transform< Scalar, Dim, Mode, Options >::shear	(	const Scalar &	sx,
		const Scalar &	sy
	)

Applies on the right the shear transformation represented by the vector other to *this and returns a reference to *this.

Warning: 2D only.

See also: preshear()

§ translate() [1/2]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Transform<Scalar,Dim>& Eigen::Transform< _Scalar, _Dim >::translate ( const MatrixBase< OtherDerived > & other )

Applies on the right the translation matrix represented by the vector other to *this and returns a reference to *this.

See also: pretranslate()

§ translate() [2/2]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

Transform<Scalar,Dim,Mode,Options>& Eigen::Transform< _Scalar, _Dim >::translate ( const MatrixBase< OtherDerived > & other )

Applies on the right the translation matrix represented by the vector other to *this and returns a reference to *this.

See also: pretranslate()

§ translation() [1/4]

template<typename _Scalar, int _Dim>

ConstTranslationPart Eigen::Transform< _Scalar, _Dim >::translation ( ) const

inline

Returns: a read-only expression of the translation vector of the transformation

§ translation() [2/4]

template<typename _Scalar, int _Dim>

TranslationPart Eigen::Transform< _Scalar, _Dim >::translation ( )

inline

Returns: a writable expression of the translation vector of the transformation

§ translation() [3/4]

template<typename _Scalar, int _Dim>

ConstTranslationPart Eigen::Transform< _Scalar, _Dim >::translation ( ) const

inline

Returns: a read-only expression of the translation vector of the transformation

§ translation() [4/4]

template<typename _Scalar, int _Dim>

TranslationPart Eigen::Transform< _Scalar, _Dim >::translation ( )

inline

Returns: a writable expression of the translation vector of the transformation

Friends And Related Function Documentation

§ operator* [1/3]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

const ProductReturnType<OtherDerived,MatrixType>::Type operator*	(	const MatrixBase< OtherDerived > &	a,
		const Transform< _Scalar, _Dim > &	b
	)

friend

Returns: the product expression of a transformation matrix a times a transform b The transformation matrix a must have a Dim+1 x Dim+1 sizes.

§ operator* [2/3]

template<typename _Scalar, int _Dim>

template<typename OtherDerived >

const internal::transform_left_product_impl<OtherDerived,Mode,Options,_Dim,_Dim+1>::ResultType operator*	(	const EigenBase< OtherDerived > &	a,
		const Transform< _Scalar, _Dim > &	b
	)

friend

Returns: the product expression of a transformation matrix a times a transform b

The left hand side other can be either:

a linear transformation matrix of size Dim x Dim,
an affine transformation matrix of size Dim x Dim+1,
a general transformation matrix of size Dim+1 x Dim+1.

§ operator* [3/3]

template<typename _Scalar, int _Dim>

template<typename DiagonalDerived >

TransformTimeDiagonalReturnType operator*	(	const DiagonalBase< DiagonalDerived > &	a,
		const Transform< _Scalar, _Dim > &	b
	)

friend

Returns: The product expression of a diagonal matrix a times a transform b

The lhs diagonal matrix is interpreted as an affine scaling transformation. The product results in a Transform of the same type (mode) as the lhs only if the lhs mode is no isometry. In that case, the returned transform is an affinity.

The documentation for this class was generated from the following file:

vendor/eigen/Eigen/src/Eigen2Support/Geometry/Transform.h

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Protected Member Functions

Protected Attributes

Friends

Detailed Description

template<typename _Scalar, int _Dim> class Eigen::Transform< _Scalar, _Dim >

Constructor & Destructor Documentation

§ Transform() [1/4]

§ Transform() [2/4]

§ Transform() [3/4]

§ Transform() [4/4]

Member Function Documentation

§ affine() [1/2]

§ affine() [2/2]

§ cast() [1/2]

§ cast() [2/2]

§ computeRotationScaling()

§ computeScalingRotation()

§ data() [1/4]

§ data() [2/4]

§ data() [3/4]

§ data() [4/4]

§ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE() [1/2]

§ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE() [2/2]

§ Identity()

§ inverse()

§ isApprox() [1/2]

§ isApprox() [2/2]

§ linear() [1/4]

§ linear() [2/4]

§ linear() [3/4]

§ linear() [4/4]

§ makeAffine()

§ matrix() [1/4]

§ matrix() [2/4]

§ matrix() [3/4]

§ matrix() [4/4]

§ operator()() [1/4]

§ operator()() [2/4]

§ operator()() [3/4]

§ operator()() [4/4]

§ operator*() [1/3]

§ operator*() [2/3]

§ operator*() [3/3]

§ operator=() [1/2]

§ operator=() [2/2]

§ prerotate() [1/2]

§ prerotate() [2/2]

§ prescale() [1/4]

§ prescale() [2/4]

§ prescale() [3/4]

§ prescale() [4/4]

§ preshear() [1/2]

§ preshear() [2/2]

§ pretranslate() [1/2]

§ pretranslate() [2/2]

§ rotate() [1/2]

§ rotate() [2/2]

§ rotation()

§ scale() [1/4]

§ scale() [2/4]

§ scale() [3/4]

§ scale() [4/4]

§ setIdentity() [1/2]

§ setIdentity() [2/2]

§ shear() [1/2]

§ shear() [2/2]

§ translate() [1/2]

§ translate() [2/2]

§ translation() [1/4]

§ translation() [2/4]

§ translation() [3/4]

§ translation() [4/4]

Friends And Related Function Documentation

§ operator* [1/3]

§ operator* [2/3]

§ operator* [3/3]

template<typename _Scalar, int _Dim>
class Eigen::Transform< _Scalar, _Dim >